I've had my current car since 2002, which I bought new for about $14,000 (including interest, which was low because I paid the car off as quickly as I possibly could, short circuiting most of the interest payments).
I go through the exercise of the total lifetime cost of my car, gas, insurance, maintenace, all told every year or two. And it's somewhere around $.30-.40 per mile or about $1 cheaper than Uber.
I recently took it in for its 130,000 mile comprehensive check over and it ended with my mechanic offering me $5,000 for the car (I didn't sell it).
It's expected that I should be able to get another 100,000 miles out of this car easily. And at my current rate of driving, that'll be an easy 10 years.
I'm pretty sure I'm going to keep this car unless it needs major mechanical repairs, and so far it hasn't.
All this means is that my cost per mile keeps going down. I'm at well under Right now I probably drive under 5,000 miles per year (telecommuting is amazing) and even these astonishingly hopeful UberX costs (60 mph commute times everywhere in cities bah!) are almost twice what it costs for me to have my own car I do whatever I want with. More realistically, these commute times could easily be tripled in most cities, making UberX even less of an option.
The only thing this answers is "will taking Uber on the occasional 25 minute or less trip cost less than owning a $50,000 MSRP luxury mid-sized sedan?" then the answer is obviously yes.
Honestly, if your starting point is a Lexus, you're not really all that concerned with your transport costs to start with.
edit I don't even think the math is right.
Let's assume his 24.2 mile commute in 25 minutes (haha!). Uber charges $1.10 + $.21 per minute or $1.31 per mile at 60mph. So let's just make the numbers easier, 25 mile commute in 25 minutes, so the commute ~ $1.31 * 25 = $32.75. But I have to go home again in the evening. * 2 = $65.50 per day. * 250 work days in the year = $16,375.
He's off by about $10,000 even assuming these ridiculous commute times.